Question

If \( AB = A \) and \( BA = B \), then \( (B^2 + B) \) equals:

• A. \( 2A \)
• B. \( O \)
• C. \( 2I \)
• D. \( 2B \)

Hint:

Matrix algebra rules, such as \( AB = A \) or \( BA = B \), often simplify to scalar multiples of matrices. Carefully verify operations.

Answer 1

The Correct Option is D

Given \( AB = A \) and \( BA = B \): \[ B^2 + B = B(B + I). \] Since \( B(B + I) = 2B \), we conclude that \( B^2 + B = 2B \).